The Israeli military’s rescue of a hostage from an underground tunnel in the Gaza Strip on Tuesday highlighted one of the biggest remaining impediments to Prime Minister Benjamin Netanyahu’s goal of eradicating Hamas: the enclave’s vast and complicated subterranean network that shelters many of the militant group’s remaining leaders.

Israel’s military said on Tuesday that it had rescued Farhan al-Qadi, a member of Israel’s Bedouin Arab minority who was abducted on Oct. 7, from an underground Hamas tunnel in southern Gaza. According to two senior officials who spoke on the condition of anonymity because they were not authorized to talk to reporters, Israeli forces appear to have found Mr. al-Qadi by chance as they were combing through a tunnel network for Hamas fighters.

It was the second time in two weeks that Hamas’s network of tunnels featured prominently in Israel’s accounts of hostage recovery efforts, shining some light on a mostly unseen aspect of the war that looms large for the country’s military and government officials. Last week, Israeli troops said they had recovered the bodies of six hostages hidden behind concrete lining in an underground route connected to a 10-meter-deep tunnel shaft.

These underground discoveries after nearly 11 months of war show just how elaborate and extensive Hamas’s tunnel network has turned out to be, experts say. Some of the tunnels are hundreds of miles long, according to Israeli, Hamas and U.S. officials.

“The tunnels are massive,” said Dan Byman, a senior fellow with the Warfare, Irregular Threats, and Terrorism Program at the Center for Strategic and International Studies in Washington. The war in Gaza has revealed two surprises about the subterranean system that Hamas built, he added: There are more tunnels, and they are more serpentine, than previously believed.

The tunnels serve Hamas in multiple ways, Mr. Byman said. Not only can the group hide its leaders and hostages in them, but capturing the tunnels — where Israeli forces are much more vulnerable and have to move very slowly — is far harder than taking a building above ground.

“The advantage of Israel’s military is tremendous coordination and situational awareness, and in tunnels that’s much harder,” he said.

Trying to destroy the subterranean system from above is also problematic, Mr. Byman said, because it takes big bombs that cause a lot of damage and potentially risk the lives of hostages hidden in the tunnels. He posited that many of the remaining living hostages were being held underground, perhaps alongside Hamas leaders, given that “they are a very valuable asset” and “one of Hamas’s chief bargaining chips.”

The Israeli military has tried several tactics during the war to drive Hamas fighters aboveground, including flooding the tunnels and sealing them, said James Wirtz, a professor of national security affairs at the Naval Postgraduate School. They also regularly explode the tunnel entrances, and send dogs, drones and robots inside them to avoid risking the life of a soldier.

“It’s horrible,” Mr. Wirtz said. “There are turns and side rooms and booby traps. It’s a hard thing to ask a soldier to do.”

The Israeli military has said it is making progress in eliminating Hamas’s underground infrastructure. On Aug. 15, the military said it had destroyed about 50 tunnels in a week, and it released video footage of soldiers blowing up burrows and building materials in an area along the border with Egypt that Israel calls the Philadelphi Corridor.

Making sure that those tunnels and others will not be rebuilt has been a critical issue in the cease-fire negotiations being mediated between Israel and Hamas. Mr. Netanyahu has said he wants some Israeli troops to continue to patrol the Philadelphi Corridor to prevent Hamas from rearming after the war or rebuilding tunnels to Egypt.

His stated goal is to eliminate Hamas, its leaders and its infrastructure, a mission that some in the Israeli military community have suggested is unrealistic. The Israeli military earlier this month said it had killed 17,000 militants in the war, but troops have repeatedly battled resurgences in areas of Gaza that it had previously declared cleared of Hamas fighters. And some of the militant group’s top leaders have survived.

In November, a freed Israeli hostage described how Yahya Sinwar, a Hamas leader who is now the group’s political chief, had addressed a large number of Israeli captives underground not long after the Oct. 7 attacks, saying that they were safe and that no harm would come to them. The United States and Israel were working hard at the time to find and capture Mr. Sinwar — and have been trying ever since.

In January, Israeli commandos raided an elaborate tunnel complex in southern Gaza based on intelligence that Mr. Sinwar was hiding there. But he had left the underground bunker days earlier and remains at large.

A public inquiry into the case of Lucy Letby, a British neonatal nurse convicted of killing seven babies, has come under fire from scientific and medical experts who have called for it to be delayed or broadened to consider whether the deaths could have been caused by other factors.

The inquiry, set to begin on Sept. 10, will cast a fresh spotlight on one of the most haunting murder cases in recent British history. Conscientious and well liked by her colleagues, Ms. Letby was found guilty of killing seven infants, and trying to kill seven others, in a busy public hospital in 2015 and 2016.

Ms. Letby, 34, was sentenced to life in prison last year and her requests for appeals have so far been denied. But questions about the handling of the investigation and the evidence used to convict her have grown harder to ignore, with prominent experts in statistics and neonatal medicine arguing that both were gravely flawed.

Under the terms of its mandate, the inquiry will not scrutinize those questions. Instead it will hold hearings to probe the experiences of the families of the babies who died and the conduct of nurses, doctors, and other health workers at the Countess of Chester Hospital, southeast of Liverpool.

Led by Kate Thirlwall, an appeals court justice, the inquiry aims to determine “whether suspicions should have been raised earlier, whether Lucy Letby should have been suspended earlier, and whether the police or other external bodies should have been informed sooner about suspicions about her.”

The thornier question — whether Ms. Letby might have been wrongfully convicted — falls beyond the scope of the inquiry, which was announced in 2023 by the health secretary in the last Conservative government.

The inquiry’s narrow scope prompted 24 experts, who emphasized that they had no connection to Ms. Letby or her family, to send a letter last month to the current health secretary, Wes Streeting, and the justice secretary, Shabana Mahmood.

In excerpts provided to The New York Times by a representative of the signatories, they wrote, “While we acknowledge the gravity of the convictions against Ms. Letby, our focus is on the broader implications for patient safety, health-care management and the potential for miscarriages of justice in complex medical cases.”

“Possible negligent deaths that were presumed to be murders could result in an incomplete investigation of the management response to the crisis,” they added, in a letter first reported by The Guardian. “Our goal is not to re-litigate the Letby case, but to ensure that the Thirlwall inquiry is positioned to conduct the most thorough and beneficial investigation possible for the future of neonatal care in the UK.”

Among the signatories are Peter Elston, a fellow of the Royal Statistical Society, and Gillian Tully, an expert in forensic science at Kings College London who served as the forensic science regulator for England and Wales. The signatories declined to release the full letter, saying it was intended to be private.

Medical experts have argued that other factors — including staff shortages, crowded conditions in the ward, poor equipment, or management problems — could have contributed to the abnormally high number of babies dying or becoming seriously ill in the unit where Ms. Letby worked. The National Health Service was under acute pressure during this period, after years of constrained budgets and understaffing.

Statisticians have criticized the investigation for concluding that because Ms. Letby was on duty during a cluster of these incidents, she must have been responsible for them.

The case hinged on her being held responsible for administering an overdose of insulin to two babies, but both survived, and several medical experts said the test results used to suggest insulin had been artificially administered were not reliable as evidence of a crime.

There were no witnesses to Ms. Letby killing or mistreating babies under her care, and she has denied murdering anyone. While her lawyers tried to discredit the prosecution’s evidence, they did not present their own evidence.

Phil Hammond, a retired doctor in the National Health Service who has written about the case as medical correspondent for Private Eye magazine, pointed out that the defense only appointed one expert and never called him. “Unsurprisingly, the evidence was very one-sided,” he said. The prosecution, he added, “were shooting at an open goal.”

Mr. Hammond has signed a separate open letter to Prime Minister Keir Starmer, which calls for a “full forensic review of the evidence used in the Letby case.” He said he was not sure whether Ms. Letby did what she was convicted of, but he does not believe she got a fair trial, a position held by a number of other people involved in the case. That could pose a challenge to an inquiry that was created on the basis that she was guilty.

Ms. Letby has been convicted twice: in August 2023, on seven counts of murder and six counts of attempted murder; and last July, on a single count of attempted murder, in a retrial after the jury did not reach a verdict on that charge in the first trial.

News coverage of the case included sensational details like her anguished handwritten notes. She wrote, “I killed them on purpose because I’m not good enough to care for them,” and in capital letters, “I AM EVIL I DID THIS.” Yet on the same piece of paper she had also scrawled: “I haven’t done anything wrong,” “I feel very alone + scared,” and “slander discrimination.”

Reporting on the case was cut off at critical junctures because of restrictions under English law on news that could prejudice a jury. Last September, the restrictions were reimposed after the public prosecutor for England and Wales announced it would seek to retry the attempted murder charge. They have since been lifted.

In May, The New Yorker published a highly critical 13,000-word investigation of the case. The magazine’s publisher, Condé Nast, blocked access to online readers in Britain, for fear of being held in contempt, which can be punished with a fine or prison sentence, although the magazine was available in print and on the magazine’s app. British papers, like The Guardian and The Times of London, have since run articles questioning the evidence, as have broadcasters.

For all the concerns being raised, however, some doubt the new Labour government will delay or expand the scope of the inquiry.

“There isn’t a political energy or head space to do it,” Mr. Hammond said. “It would be so embarrassing if the biggest baby-killer case in British history was found to be unsound.”

A Ukrainian F-16, recently supplied by NATO countries, was destroyed this week while defending against a sweeping Russian aerial assault and the pilot was killed, Ukraine’s military said on Thursday.

The loss is a blow to the government in Kyiv, partly because only about half a dozen of the planes have been delivered and only a few pilots have been trained to fly them.

The timing of the crash was unfortunate as well, coming after a Ukrainian incursion into Russia’s Kursk region had lifted the national mood this month after a long spring and summer of Russian battlefield gains in eastern Ukraine.

Ukraine received its first batch of F-16s this summer after the country’s leaders argued to the White House and allies in Europe for many months that they were essential to the war effort. While the United States and other allies have provided Ukraine with tens of billions of dollars of military equipment, the fighter jets have taken on outsize importance as a symbol of Western support.

However, military experts have cautioned that the jets are unlikely to make an immediate difference on the battlefield, even though they are versatile and equipped with advanced radar systems and a variety of weapons. Their primary value, the experts said, will be their role in defending Ukraine in the coming years.

The plane was lost after Ukraine scrambled its air defenses while trying to intercept more than 200 missiles and drones fired by Russia on Monday, in what President Volodymyr Zelensky of Ukraine called one of the largest attacks of its kind since the war began 30 months ago.

The F-16s were involved in the effort and had “demonstrated their high efficiency,” shooting down four cruise missiles, Ukraine’s general staff said on Facebook on Thursday. But “communication was lost with one of the aircraft. It was later determined that the aircraft had crashed and the pilot was killed.”

The military said that it had opened an investigation into the crash, which was reported Thursday by The Wall Street Journal. A Western official said the Ukrainians were looking at pilot error or mechanical failure as the cause for the crash, rather than enemy fire. The military general staff did not disclose the identity of the pilot who was killed, but Ukraine’s Air Force said that it had lost a pilot named Oleksiy Mes on Monday during the assault on the country.

“Oleksiy saved Ukrainians from deadly Russian missiles. Unfortunately, at the cost of your own life,” the Air Force’s western command said in a Facebook post that addressed the pilot.

A news website in the city of Lutsk in northwestern Ukraine, Volyn News, reported that a large funeral was held in the city on Thursday for the pilot. It posted photographs of the event and said that Ukrainian Air Force jets performed a fly over in honor of the pilot. The website said his call sign was Moonfish. Ukrainian combat pilots, a select group, are considered heroes by many in Ukraine for the risks they have taken to fight the invasion, and Mr. Mes’ death will likely be widely mourned.

The arrival and deployment of the F-16s has been a subplot in the war. From the earliest days of the full-scale invasion in February 2022, Mr. Zelensky had called on NATO to supply his country with the most advanced and powerful conventional weapons, arguing that Ukraine was fighting for all of Europe as well as Western values.

Each time President Biden and other leaders acceded to Kyiv’s requests, Ukrainian leaders expressed gratitude while also making new demands. The fighter jets, which can be used to attack Russian forces but are also valuable for their ability to shoot down incoming missiles, became the most high-profile item on Ukraine’s list.

When they finally arrived, Mr. Zelensky posted a triumphant video on his social media page and was photographed sitting in one.

Ukrainian officials declined to say how many planes had been delivered in the initial batch, but European countries, which have promised 45 of the jets, were expected to deliver only six this summer.

Romania had set up a school to train Ukrainian pilots — an arduous process, given the planes’ complexity — but by March it was clear that only 12 pilots would be ready by the summer. The pilots also received training in Denmark, the United States and Britain.

Their arrival in early August to supplement the country’s fleet of Soviet-era aircraft had given a lift to national morale at a time of significant developments in the war.

For much of the year, Ukrainian forces have been on the defensive in the country’s east in the face of a Russian onslaught that has steadily, if slowly, made progress. Russian troops seized control of two cities in Donetsk region early in the year after months of fierce fighting, and in recent weeks they have put the city of Pokrovsk, an important transport hub for Ukraine’s military, under increasing pressure.

Anastasia Kuznietsova contributed reporting from Kyiv, Ukraine.

A Greek oil tanker is stuck in the Red Sea after it was attacked by Houthi rebels, an Iran-backed militia group that controls swaths of northern Yemen and has disrupted crucial shipping lanes in a show of solidarity with Palestinians in Gaza.

The MV Delta Sounion has been immobilized for more than a week, making it a sitting duck for further attacks while also raising fears of an environmental disaster. The tanker was carrying the equivalent of one million barrels of crude oil.

The Sounion, its crew evacuated, currently sits in waters patrolled by Houthi vessels. The Houthis have said they will allow a rescue mission, but moving the ship will be precarious.

Here’s what we know about the stuck tanker.

How did the ship get stuck?

The MV Delta Sounion was sailing through the southern Red Sea when it came under attack from vessels controlled by Houthi fighters on Aug. 21, according to the European Union’s naval mission in the Red Sea, the Indian Ocean and the Gulf.

No crew members were killed or injured, but the ship lost engine power during the attack, the naval mission said on social media. The crew of 23 Filipino and two Russian sailors was evacuated to Djibouti, a country on the Horn of Africa.

During the rescue, the naval mission’s ship spotted an unmanned vessel nearby, and immediately destroyed it. In past attacks, Houthi rebels have used remote-controlled boats that have rushed at vessels, causing explosive collisions.

The Sounion, flying a Greek flag and managed by the Greek shipping company Delta Tankers, had been traveling from Iraq to Greece, according to a briefing from the Pentagon. Now, it poses a navigational hazard to other ships passing through the area, the Pentagon said.

In a statement on Thursday, Greece’s foreign minister, George Gerapetritis, said he had spoken to his counterpart in Saudi Arabia, which has a coast along the Red Sea, “to ensure the safest possible management of this issue.”

What is the environmental risk?

The ship’s cargo contains 150,000 tons of crude oil, or more than a million barrels. What’s worse, the stranded ship has been on fire since Aug. 23, posing an “imminent threat of regional pollution,” the European Union naval mission said.

On Wednesday, aerial images of the Sounion showed several fires on the deck. While there is no apparent oil leak yet, the Pentagon raised concerns on Tuesday that the stranded vessel represented a “potential environmental catastrophe.” (The U.S. State Department has said the spill of a million barrels of oil would be four times the size of the 1989 Exxon Valdez disaster in Alaska.)

International naval forces and agencies are working together to determine how to move the nearly 900-foot-long tanker.

Why are the Houthis attacking ships?

The Houthis are a group of Shiite militants who have fought Yemen’s government for more than two decades. With the support of Iran, the group now controls large swathes of northern Yemen and it has become the de facto government in the Gulf country. The U.S. designated the group a terrorist organization in February.

In recent years, the group has been targeting vessels traveling in the Gulf of Aden and the Red Sea, a crucial gateway for global shipping through the Suez Canal. After Hamas’s Oct. 7 attack on Israel and the ensuing war in Gaza, the Houthis pledged their solidarity to the Palestinian people, stepping up attacks on ships and disrupting international shipping lanes.

On Wednesday, a Houthi spokesman, Mohammed Abdulsalam, told Iranian media that it would allow the retrieval of the Sounion, acquiescing to requests from several countries. Iran’s mission to the United Nations confirmed the decision, adding that the group had consented because of humanitarian and environmental concerns.

Still, Houthi leaders have vowed to continue their campaign to disrupt shipping lanes, according to the Site Intelligence Group, which tracks extremist organizations.

“These are simply reckless acts of terrorism which continue to destabilize global and regional commerce, put the lives of innocent civilian mariners at risk, and imperil the vibrant maritime ecosystem in the Red Sea and Gulf of Aden, the Houthis own backyard,” Maj. Gen. Pat Ryder, a Pentagon spokesman, said during a news briefing on Tuesday.

Ephrat Livni contributed reporting.

The White House national security adviser, Jake Sullivan, met on Thursday with China’s leader, Xi Jinping, and held rare talks with a top Chinese military official in a sign that the two countries are communicating at senior levels despite tensions over the South China Sea and Taiwan.

Mr. Sullivan’s meeting with Gen. Zhang Youxia, vice chairman of China’s Central Military Commission, was the first in years between a senior American official and a vice chair of the commission, which oversees China’s armed forces and is chaired by Mr. Xi. In 2018, Jim Mattis, who was the U.S. defense secretary at the time, met with Gen. Xu Qiliang, who held the vice chair position.

It was the latest effort by the two powers to keep communication channels open even as disputes grow over national security, trade and geopolitics. On the military front, the United States has argued that more open communication is necessary to prevent accidents between the two countries’ warplanes and navy ships as they regularly patrol contested areas like the Taiwan Strait and the South China Sea.

“A meeting with Zhang Youxia is very significant, and an indication that China is prepared to meaningfully re-engage with the Department of Defense,” said Drew Thompson, a visiting senior research fellow at the Lee Kuan Yew School of Public Policy at the National University of Singapore. “Beijing views the military-to-military relationship as an important political indicator of the overall relationship, which differs somewhat from the U.S. perspective, which sees it as a more pragmatic channel to reduce risk.”

Mr. Sullivan’s meeting with General Zhang, which was held at the headquarters of China’s People’s Liberation Army, came on the final day of his three-day visit to Beijing to bolster the Biden administration’s bid to manage competition with China.

China and the United States have been locked in a rivalry for global influence and have seen tensions rise over a raft of issues, including China’s territorial claims in the South China Sea, its tacit support for Russia’s war in Ukraine, and the flood of Chinese electric vehicles and solar panels onto global markets.

“We believe that competition with China does not have to lead to conflict and confrontation — the key is responsible management through diplomacy,” Mr. Sullivan said at a news conference after meeting with Mr. Xi.

Even as the visit was a chance for both nations to reassure the world that they were working to lower the risk of conflict between them, it was clear that they were still fundamentally divided on strategic issues. China has rejected Washington’s framing of the bilateral relationship as being defined by competition, a stance Mr. Xi highlighted at the top of an official summary of the meeting.

“First of all, we must answer the general question of whether China and the United States are rivals or partners,” Mr. Xi told Mr. Sullivan. China’s intentions were “above board,” he said, and his country was committed to “peaceful development.” He said he hoped that the United States would work with China to “find a correct way for the two major countries to get along.”

Mr. Sullivan told reporters that the Biden administration’s priorities in its final months included greater communication between their militaries and more cooperation to tackle the fentanyl crisis in the United States.

He also elaborated on discussions about a potential meeting between President Biden and Mr. Xi, noting that both leaders would likely attend the Asia-Pacific Economic Cooperation summit in Peru and the Group of 20 Leader’s Summit in Brazil, to be held in mid-November.

“It would only be natural for them to have the chance to sit down with one another,” Mr. Sullivan said.

He also spoke briefly about Vice President Kamala Harris, who is now the Democratic Party’s presidential candidate, and her perspective on China.

“She shares President Biden’s view that responsibly managing this competition, so it doesn’t veer into conflict or confrontation, is essential,” Mr. Sullivan told reporters, noting that Ms. Harris has met Mr. Xi and also China’s second-highest official, Premier Li Qiang.

Earlier in the day, General Zhang told Mr. Sullivan that the world expected the two countries to “maintain stability in the military and security fields,” according to a statement released by China’s defense ministry. He also reiterated China’s opposition to American support for Taiwan, the island democracy that Beijing claims.

“China demands that the United States stop military collusion between the United States and Taiwan, stop arming Taiwan, and stop spreading false narratives involving Taiwan,” the general said, according to the official statement.

Mr. Sullivan later said that having a chance to speak in person with General Zhang had made a difference.

“The meeting with Vice Chairman Zhang was very important — there is no substitute for actually being able to sit across the table not just with the vice chairman but with his whole team, to be able to hear from them their perspective on critical issues,” he said.

On Wednesday, Mr. Sullivan and China’s most senior diplomatic official, Wang Yi, said their countries’ top military commanders in the region would hold a video call at some point.

Mr. Thompson said such a call could help reinvigorate lower-level dialogue that used to take place more frequently in the past. Those meetings, he said, allowed military personnel to discuss aerial and maritime maneuvers in greater detail to prevent accidents.

Washington is also concerned about encounters between China and U.S. allies that could draw American forces into a confrontation. That includes the most recent standoff between the Philippines and China near a disputed atoll, Sabina Shoal, where Chinese coast guard vessels have rammed Philippine ships and targeted them with water cannons.

“The order of the day should be de-escalation” in the South China Sea, said Mr. Sullivan, who, during his talks in Beijing, raised America’s commitment to defend the Philippines as a treaty ally.

“Nobody is looking for a crisis — not the Philippines, not the United States and, we hope, not the P.R.C.,” he said, referring to the People’s Republic of China.

Such regional tensions have led to chilly relations between the Pentagon and the Chinese military over the past several years. China suspended military-to-military communications in 2022 after Nancy Pelosi, who was speaker of the House at the time, visited Taiwan. They were restored in December when President Biden’s senior military adviser, Gen. Charles Q. Brown, held a videoconference call with his Chinese counterpart, Gen. Liu Zhenli.